Viral Infection Model with Diffusion and Distributed Delay: Finite-Dimensional Global Attractor.

Area of Science:

• Mathematical Biology
• Virology
• Dynamical Systems Theory

Background:

• Understanding virus dynamics is crucial for disease control.
• Reaction-diffusion models with logistic growth capture spatial spread and population limits.
• Non-linear infection rates and distributed delays add complexity to biological realism.

Purpose of the Study:

• To investigate a sophisticated virus dynamics model incorporating reaction-diffusion, logistic growth, and a general non-linear infection rate.
• To analyze the impact of distributed delays, including state-selective delays, on viral spread.
• To establish the existence of a finite-dimensional global attractor for the proposed dynamical system.

Main Methods:

• Formulation of a virus dynamics model with reaction-diffusion and logistic growth.
• Inclusion of a general non-linear functional response for infection rate.
• Mathematical analysis within a Hilbert space framework to construct the dynamical system.
• Proof of the existence of a finite-dimensional global attractor.

Main Results:

• Demonstration of the existence of a global attractor for the virus dynamics model.
• The attractor is shown to be finite-dimensional, simplifying the long-term behavior analysis.
• The model successfully incorporates complex factors like non-linear infection and distributed delays.

Conclusions:

• The study confirms the existence of a finite-dimensional global attractor for the complex virus dynamics model.
• This finding provides a theoretical foundation for understanding the long-term behavior and stability of viral infections.
• The mathematical framework developed can be applied to analyze other complex biological systems with delays and non-linearities.